[Ed Wright]

The O2 sensor has about zero effect on cold starts. Those older TBI trucks do not have heated O2 sensors, thus don't go into Closed Loop nearly as soon as later models. Sounds more like when it goes into Closed Loop it is correcting it's self. If it was the O2 sensor it would be more prone to go rich after it went into closed loop. Not on cold starts.
First, I would pull the air filter, and have somebody turn the key on, and watch for leaking injectors.
Next, with the truck "cold soaked", (having sat for 8 hours or so), hook up your scan tool. Just turn the key on. Verify the displayed temp is very close to the ambient temp. If it indicates a good bit colder than actual temp where the truck is sitting, that is likely your problem. Seen this many times. Same effect as the choke set too tight on a carb. When it goes into Closed Loop it will lean it's self back to 14.7-1. If the indicated coolant temp is skewed low, it will also go into closed loop later than normal, causing the rich condition to last longer.
High resistance in the coolant temp circuit will cause lower than actual temps seen by the ECM. Unplug the coolant sensor, the ECM "sees" -40 degrees F.

High fuel pressure will cause the same thing. This will also cause low BLM & INT numbers on your scan tool in closed loop. Neutral values for those parameters would be 128. Lower numbers indicate pulling fuel to correct for a perceived rich condition. Higher indicates adding fuel for a perceived lean condition.